HYPERSPHERICAL KINEMATIC VIBRATIONAL COORDINATES FOR LINEAR TRIATOMIC-MOLECULES

A set of hyperspherical kinematic coordinates is used to describe the molecular vibrations of linear triatomic molecules. These coordinates are derived by expressing first the internal mass-scaled orthogonal ve ctors, which include as particular cases the Jacobi and Radau vectors, in terms of the so-called kinematic angle, which is assumed to be an optimization parameter. The magnitudes of the internal orthogonal vect ors and the angle between them define a set of kinematic vibrational c oordinates, which is then transformed into generalized hyperspherical coordinates. This hyperspherical transformation depends on two displac ement parameters which specify the orientation and curvature of the po lar variables. The resulting hyperspherical kinematic system contains, therefore, three optimization parameters. For linear triatomic molecu les this system can be chosen to be a curvilinear normal system by pro per selection of the displacement parameters. The utility of the hyper spherical kinematic coordinates is illustrated by carrying out vibrati onal calculations of vibrational energy levels for OCS and N2O. The en ergies obtained are also compared with the experimental values.